共振非线性薛定谔方程中的孤立波：稳定性和动力学性质
Solitary waves in the resonant nonlinear Schrödinger equation: stability and dynamical properties
摘要：
研究了共振非线性薛定谔（RNLS）方程的稳定性和动力学性质。RNLS是非线性薛定谔（NLS）方程的一个变体，增加了一个用于描述冷无碰撞等离子体中波传播的微扰。我们首先研究RNLS模型中平面波的调制稳定性，确定从NLS情况下的相关条件的修改。然后，我们转移到孤立波与消失和非零边界条件的研究。有趣的是，RNLS，很像通常的NLS，表现出暗和亮孤子解决方案取决于色散和非线性的相对符号。本文系统地研究了这些解的存在性、稳定性和动力学性质。
英文摘要：
The stability and dynamical properties of the so-called resonant nonlinear Schrödinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schrödinger (NLS) equation with the addition of a perturbation used to describe wave propagation in cold collisionless plasmas. We first examine the modulational stability of plane waves in the RNLS model, identifying the modifications of the associated conditions from the NLS case. We then move to the study of solitary waves with vanishing and nonzero boundary conditions. Interestingly the RNLS, much like the usual NLS, exhibits both dark and bright soliton solutions depending on the relative signs of dispersion and nonlinearity. The corresponding existence, stability and dynamics of these solutions are studied systematically in this work.
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